This application claims priority on Japanese Patent Application No. 2001-131833 filed on Apr. 27, 2001 the contents of which are incorporated herein by reference.
1. Field of the Invention
The present invention relates to a method of machining a screw-shaped portion or screw groove in a workpiece, particularly, when a female screw groove is ground by means of a machine tool, such as a grinder.
2. Description of the Related Art
Various methods for machining a female (or internal) screw thread-groove by grinding are, as schematically shown in FIGS. 12A-C, already known. In the method shown in FIG. 12A, an internal grinding wheel spindle 101 is tilted relative to a workpiece 102 at the same angle as the lead angle xcex1 of the screw groove while the workpiece is machined with a grinding wheel 103 mounted on one end of a grinding wheel quill 104. According to this method, the grinding wheel 103 is shaped by a form rotary dresser that has an identical contour to that of the female thread-groove to be machined.
In the method shown in FIG. 12B, the internal grinding wheel spindle 101 is tilted relative to the workpiece 102 at an angle, "xgr", which is smaller than the lead angle xcex1 of the screw thread while the workpiece is machined with a grinding wheel 103. In this case, the grinding wheel 103 is machined with a form rotary dresser whose shape corresponds to the shape of the female groove to be machined. More particularly, after the shape of the female thread-groove is determined, numerous form rotary dressers are machined until one with an optimal shape is obtained through corrections and adjustments.
The method illustrated in FIG. 12C is disclosed in Japanese Published Examined Patent Application No. 8-11329, in which the internal grinding wheel spindle 101 is disposed in parallel to the axis of the workpiece 102 during the machining of the desired female groove. According to this method, the shape of the grinding wheel 103 is first calculated from data representing specifications of the female thread-groove. The grinding wheel 103 is then machined by a single point dresser under synchronous numerical control on the basis of data representing the calculated grinding wheel shape. When the lead angle xcex1 is large or when deep grinding is required, this method has the advantage over the one shown in FIG. 12A of being capable of avoiding interference between the grinding wheel quill 104 and the female screw groove.
While achieving their intended objectives, the foregoing conventional methods suffer from a number of deficiencies that reduce their utility. For example, the method of FIG. 12A, which is very commonly practiced, has an inherent problem in that a female screw groove cannot be machined if the lead angle xcex1 of the screw thread is very large or if deep grooving is required, as the wheel quill 104 interferes with the thread-groove, thus limiting the machinable ranges.
The method of FIG. 12B is often employed if the lead angle xcex1 of the female screw thread is relatively large with respect to the hole diameter bored in the workpiece. In contrast to the method of FIG. 12A, this particular method reduces the interference between the grinding wheel quill 104 and the hole in the workpiece, thereby enabling machining of female screws with larger lead angles xcex1 and greater depths. However, machining female screws by this method proves a time-consuming process as much trial and error is required to determine a suitable shape for the grinding wheel.
If the third known method (FIG. 12C) is employed to grind a female screw with a large lead angle xcex1, considerable interference occurs between the female screw groove and the grinding wheel 103, requiring reduction in the diameter of the grinding wheel and thus the diameter of the wheel quill 104.
In view of the above-identified problems, an important object of the present invention is to provide a method of correctly shaping an internal grinding wheel without trial and error and machining a female screw in a workpiece, while the axis of the wheel spindle tilted relative to the axis of the workpiece at an angle smaller than the lead angle of the screw thread.
Another important object of the present invention is to provide a method of grinding a female screw with an internal grinding wheel spindle machined without trial and error as above.
Another important object of the present invention is to provide a method of dressing, without trial and error, an internal grinding wheel suitable for machining a female screw groove in a workpiece while the axis of the wheel spindle tilted relative to the axis of the workpiece at an angle smaller than the lead angle of the screw thread to be machined.
The above objects and other related objects are realized by the invention, which provides a method of machining a female screw groove in a hole in a female screw workpiece extending along a z-axis with an internal grinding wheel coupled to a spindle having an axis, with the axis of the spindle being tilted relative to the z-axis at an angle smaller than the lead angle of the female screw thread, whereby relative rotation is caused between the workpiece and the grinding wheel while relative movement is caused between the grinding wheel and the workpiece along the z-axis and along an x-axis normal to the z-axis. The method comprises the steps of: (A) providing data representing specifications of the female screw and the tilt angle of the axis of the wheel spindle relative to the z-axis; (B) obtaining data on dressing the grinding wheel from the data representing the specifications of the female screw and the tilt angle of the wheel spindle axis; (C) dressing the grinding wheel on the basis of the obtained dressing data by simultaneous triaxial control of relative movement between the grinding wheel and a single point dresser along the z-axis of the workpiece and the x-axis, and rotation of a tip of the single point dresser about a b-axis in the plane defined by the x- and z-axes; and (D) machining the female screw groove with the dressed grinding wheel.
According to the conventional method whereby the spindle axis is maintained parallel to the axis of the workpiece, the diameter of the grinding wheel must be decreased as the lead angle of the female screw thread increases, which in turn reduces the diameter of the wheel spindle, thus sacrificing the rigidity of the spindle. According to the method of the invention, however, the spindle of the internal grinding wheel is disposed at a smaller angle relative to the axis of the spindle than the lead angle of the female screw thread throughout the machining operation, such that a relatively large-diameter grinding wheel with an accordingly large-diameter spindle can be employed so as to prevent reduction in the spindle rigidity resulting from a small spindle diameter.
According to one aspect of the present invention, the grinding wheel has a width along the axis of the wheel spindle and the workpiece is machined to a female ball screw with a Gothic arc profile, and the specifications of the female screw includes data representing: the lead of the female screw; the radius of the Gothic arc; a Gothic arc offset value; the diameter of the female ball screw as measured between the centers of diametrically opposing balls; and the diameter of the cross-section of the grinding wheel located at the center of the wheel""s width and oriented normal to the wheel spindle axis.
According to another aspect of the present invention, the grinding wheel has a diameter that changes along the axis of the wheel spindle, and additionally, the step of obtaining data for dressing the grinding wheel includes the steps of:
a) calculating the distance from the center of a ball to a bottom of the screw groove and the coordinates of the center of the grinding wheel on a cross-section normal to the wheel spindle axis;
b) determining the polar coordinates of the locus of the female screw groove on a cross-section normal to the axis of the workpiece from the distance calculated in step (a);
c) calculating from the polar coordinates determined in step (b) the sinusoidal locus of the female screw groove projected onto a cross-section in which the axis of the workpiece is located;
d) calculating the coordinates of the intersection of the sinusoidal locus and the wheel cross-section normal to the spindle axis;
e) calculating the diameter of the grinding wheel on the wheel cross-section normal to the spindle axis from the coordinates calculated in step (d) and the coordinates calculated in step (a); and
f) repeating steps (a)-(e) so as to calculate the diameter of the grinding wheel on a plurality of cross-sections normal to the axis of the wheel spindle, thus determining an outer shape of the grinding wheel.
According to still another aspect of the present invention, the internal grinding wheel, the spindle thereof, and the single point dresser constitute part of a numerically controlled grinder including a processing unit, and additionally, the step of providing data includes the step of entering the data representing the specifications of the female screw and the tilt angle into the processing unit of the numerically controlled grinder, whereas the step of obtaining data for dressing the grinding wheel includes the step of executing in the processing unit a computer program for generating data on an outer shape of the grinding wheel from the data representing the specifications of the female screw and the tilt angle of the spindle axis.
According to yet another aspect of the present invention, the step of executing a computer program includes the step of compensating the data on the outer shape for the tilt angle of the axis of the grinding wheel spindle.
The foregoing method permits (1) automatic generation of data on the geometry of a grinding wheel tilted, during machining, with respect to the spindle axis at an angle smaller than the screw""s lead angle based on certain specifications of the female screw and the tilt angle of the spindle axis and (2) generation of data for dressing a grinding wheel by additional processing of the data on the geometry of the grinding wheel.
The invention further provides a method of dressing with a single point dresser an internal grinding wheel for machining a female screw, the grinding wheel including a spindle which has an axis tilted during dressing relative to a z-axis of a workpiece at an angle smaller than the lead angle of the female screw to be machined in the workpiece, the method comprising the steps of:
I. providing data representing specifications of the female screw and the tilt angle of the spindle axis relative to the z-axis of the workpiece;
II. calculating data representing an outer shape of the grinding wheel from the data representing specifications of the female screw and the tilt angle of the wheel spindle axis;
III. generating, from the data calculated in step II, data representing (i) relative movement between the single point dresser and the grinding wheel along the z-axis and an x-axis normal to the z-axis and (ii) simultaneous rotation of a tip of the single point dresser in the plane defined by the x- and y-axes about a b-axis normal to the x-y plane; and
IV. dressing the grinding wheel on the basis of the data generated in step (III).
According to one feature of the present invention, the grinding wheel has a width along the axis of the wheel spindle and the workpiece is machined to a female ball screw with a Gothic arc profile, and further wherein the specifications of the female screw includes data on: the lead of the female screw; the radius of the Gothic arc; a Gothic arc offset value; the diameter of the female ball screw as measured between the centers of diametrically opposing balls; and the diameter of the cross-section of the grinding wheel located at the center of the wheel""s width and oriented normal to the wheel spindle axis.
In one embodiment, the grinding wheel has a diameter that changes along the axis of the wheel spindle, and further wherein the step of calculating data representing an outer shape of the grinding wheel includes the steps of:
a) calculating the distance from the center of a ball to a bottom of the screw and the coordinates of the center of the grinding wheel on a cross-section normal to the wheel spindle axis;
b) determining the polar coordinates of the locus of the female screw groove on a cross-section normal to the axis of the workpiece from the distance calculated in step (a);
c) calculating from the polar coordinates determined in step (b) the sinusoidal locus of the female screw groove projected onto a cross-section in which the axis of the workpiece is located;
d) calculating the coordinates of the intersection of the sinusoidal locus and the wheel cross-section normal to the spindle axis;
e) calculating the diameter of the grinding wheel on the wheel cross-section normal to the spindle axis from the coordinates calculated in step (d) and the coordinates calculated in step (a); and
f) repeating steps (a)-(e) so as to calculate the diameter of the grinding wheel on a plurality of cross-sections normal to the axis of the wheel spindle, thus determining an outer shape of the grinding wheel.
In another embodiment, the internal grinding wheel, the spindle thereof, and the single point dresser constitute part of a numerically controlled grinder including a processing unit, and additionally, step (I) includes the step of entering the data representing the specifications of the female screw and the tilt angle into the processing unit of the numerically controlled grinder, and step (II) includes the step of executing in the processing unit a computer program for generating data on an outer shape of the grinding wheel from the data representing the specifications and the tilt angle.
The inventor proposed in Japanese Published Examined Patent Application No. 8-11329 (briefly described above) a method of machining a workpiece with an internal grinding wheel with the axis of the wheel disposed in parallel to the axis of the workpiece whereby the outer shape of the grinding wheel is computed by mathematical expressions. According to the present invention, this technology is further developed (1) to compute data on the outer shape of a grinding wheel for machining a female screw groove in a workpiece, with the axis of the grinding wheel spindle tilted at an angle smaller than the lead angle of the screw thread relative to the workpiece axis throughout machining and (2) to perform automatic dressing of the grinding wheel by executing simultaneous triaxial control of a machine tool on the basis of the data thus generated.
Other general and more specific objects of the invention will in part be obvious and will in part be evident from the drawings and descriptions which follow.